import numpy as np
import pandas as pd

# sklearn
from sklearn.metrics import confusion_matrix
from sklearn.model_selection import train_test_split
from sklearn.datasets import make_moons, make_circles, make_classification

# Tensorflow
import tensorflow as tf
from tensorflow import keras
from tensorflow.keras import layers

# Visualisation libraries

## matplotlib
import matplotlib.pyplot as plt
%matplotlib inline

## seaborn
import seaborn as sns
sns.set_context("paper", rc={"font.size":12,"axes.titlesize":14,"axes.labelsize":12})
sns.set_style("white")

## plotly
from plotly.offline import init_notebook_mode, iplot 
import plotly.graph_objs as go
import plotly.offline as py
from plotly.subplots import make_subplots
import plotly.express as px
import plotly.figure_factory as ff
%config InlineBackend.figure_format = 'retina' 

import warnings
warnings.filterwarnings("ignore")

Deep Neural Network (DNN)

Machine learning can be categorized as supervised, semi-supervised, or unsupervised learning methods. Deep learning can be supervised or unsupervised, and it is based on artificial neural networks (ANN) with representation learning. In this article, we demonstrate implementing a deep neural network (DNN) in Keras.

Deep Neural Networks (DNNs), which is also known as convolutional networks, is comprised of several layers of nonlinear operations. The goal of deep learning methods is to learn feature hierarchies. Higher levels of features are formed by combining lower level features [1].

Dataset

a random n-class classification dataset can be generated using sklearn.datasets.make_classification. Here, we generate a dataset with two features and 5000 instances. Moreover, dataset is generated for a multiclass modeling.

X, y = make_classification(n_samples = int(5e3), n_features=2, n_redundant=0,
                           n_informative=2, random_state=1, n_clusters_per_class=1)
y = y.reshape(-1,1)
Labels = np.unique(y)
Labels = [str(x) for x in Labels]

Modeling

Train and Test sets

One of the efficient methods of splitting a dataset into random train and test subsets is using sklearn.model_selection.train_test_split.

X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.3, random_state=42)
y = y.reshape(-1,1)

pd.DataFrame(data={'Set':['X_train','X_test','y_train','y_test'],
               'Shape':[X_train.shape, X_test.shape, y_train.shape, y_test.shape]}).set_index('Set').T

Set	X_train	X_test	y_train	y_test
Shape	(3500, 2)	(1500, 2)	(3500, 1)	(1500, 1)

Multi-layer Perceptron (MLP) for Binary classification

A multi-layer perceptron (MLP) is a class of feedforward artificial neural network (ANN). scikit-learn.org has a well-written article regarding MLP and interested readers are encouraged to see this article.

In this article, an MLP for binary classification using Keras is presented. We define our model by using Sequential class. Moreover, we consider the rectified linear unit) (ReLU) as the activation function. An activation function allows for complex relationships in the data to be learned. For the last year, we use the Sigmoid function. Some examples of Sigmond functions can be found here.

model = keras.Sequential(name = 'Binary_MLP')
model.add(layers.Dense(64, input_dim = X.shape[1], activation='relu', name='Layer1'))
model.add(layers.Dropout(0.5))
model.add(layers.Dense(64, activation='relu', name='Layer2'))
model.add(layers.Dropout(0.5))
model.add(layers.Dense(1, activation='sigmoid', name='Layer3'))
model.summary()
tf.keras.utils.plot_model(model, show_shapes=True, show_layer_names=True, expand_nested = True, rankdir = 'LR')

Model: "Binary_MLP"
_________________________________________________________________
Layer (type)                 Output Shape              Param #   
=================================================================
Layer1 (Dense)               (None, 64)                192       
_________________________________________________________________
dropout (Dropout)            (None, 64)                0         
_________________________________________________________________
Layer2 (Dense)               (None, 64)                4160      
_________________________________________________________________
dropout_1 (Dropout)          (None, 64)                0         
_________________________________________________________________
Layer3 (Dense)               (None, 1)                 65        
=================================================================
Total params: 4,417
Trainable params: 4,417
Non-trainable params: 0
_________________________________________________________________

# Number of iterations
IT = int(5e2)+1

model.compile(optimizer= 'rmsprop', loss='binary_crossentropy', metrics=['accuracy','mae', 'mse'])

# Train model
history = model.fit(X_train, y_train, validation_data=(X_test, y_test), epochs= IT, batch_size=128, verbose = 0)

def Search_List(Key, List): return [s for s in List if Key in s]

Metrics_Names = {'loss':'Loss', 'accuracy':'Accuracy', 'mae':'MAE', 'mse':'MSE'}

def Table_modify(df, Metrics_Names = Metrics_Names):
    df = df.rename(columns = Metrics_Names)
    df = df.reindex(sorted(df.columns), axis=1)
    df.insert(loc = 0, column = 'Iteration', value = np.arange(0, df.shape[0]), allow_duplicates=False)
    return df

Validation_Table = Search_List('val_',history.history.keys()) 
Train_Table = list(set( history.history.keys()) - set(Validation_Table))
Validation_Table = pd.DataFrame(np.array([history.history[x] for x in Validation_Table]).T, columns = Validation_Table)
Train_Table = pd.DataFrame(np.array([history.history[x] for x in Train_Table]).T, columns = Train_Table)
Validation_Table.columns = [x.replace('val_','') for x in Validation_Table.columns]

Train_Table = Table_modify(Train_Table)
Validation_Table = Table_modify(Validation_Table)

# Train Set Score
score = model.evaluate(X_test, y_test, batch_size=128, verbose = 0) 
score = pd.DataFrame(score, index = model.metrics_names).T
score.index = ['Train Set Score']
# Validation Set Score
Temp = model.evaluate(X_train, y_train, batch_size=128, verbose = 0) 
Temp = pd.DataFrame(Temp, index = model.metrics_names).T
Temp.index = ['Validation Set Score']
score = score.append(Temp)
score.rename(columns= Metrics_Names, inplace = True)
score = score.reindex(sorted(score.columns), axis=1)
display(score.style.set_precision(4))

	Accuracy	Loss	MAE	MSE
Train Set Score	0.9080	0.2210	0.1384	0.0660
Validation Set Score	0.9091	0.2281	0.1384	0.0683

Let's define some function by which we can analyze the performance of the modeling.

def Plot_history(history, Title = False, Table_Rows = 25):
    fig = make_subplots(rows=1, cols=2, horizontal_spacing = 0.02, column_widths=[0.6, 0.4],
                        specs=[[{"type": "scatter"},{"type": "table"}]])
    # Left
    fig.add_trace(go.Scatter(x= history['Iteration'].values, y= history['Loss'].values,
                             line=dict(color='OrangeRed', width= 1.5), name = 'Loss'), 1, 1)
    fig.add_trace(go.Scatter(x= history['Iteration'].values, y= history['Accuracy'].values,
                             line=dict(color='MidnightBlue', width= 1.5),  name = 'Accuracy'), 1, 1)
    fig.add_trace(go.Scatter(x= history['Iteration'].values, y= history['MAE'].values,
                             line=dict(color='ForestGreen', width= 1.5), name = 'Mean Absolute Error (MAE)'), 1, 1)
    fig.add_trace(go.Scatter(x= history['Iteration'].values, y= history['MSE'].values,
                             line=dict(color='purple', width= 1.5), name = 'Mean Squared Error (MSE)'), 1, 1)
    fig.update_layout(legend=dict(x=0, y=1.1, traceorder='reversed', font_size=12),
                  dragmode='select', plot_bgcolor= 'white', height=600, hovermode='closest',
                  legend_orientation='h')
    fig.update_xaxes(range=[history.Iteration.min(), history.Iteration.max()],
                     showgrid=True, gridwidth=1, gridcolor='Lightgray',
                     showline=True, linewidth=1, linecolor='Lightgray', mirror=True, row=1, col=1)
    fig.update_yaxes(range=[0, 1], showgrid=True, gridwidth=1, gridcolor='Lightgray',
                     showline=True, linewidth=1, linecolor='Lightgray', mirror=True, row=1, col=1)
    # Right
    ind = np.linspace(0, history.shape[0], Table_Rows, endpoint = False).round(0).astype(int)
    ind = np.append(ind, history.Iteration.values[-1])
    history = history[history.index.isin(ind)]
    Temp = []
    for i in history.columns:
        Temp.append(history.loc[:,i].astype(float).round(4).values) 
    fig.add_trace(go.Table(header=dict(values = list(history.columns), line_color='darkslategray',
                                       fill_color='DimGray', align=['center','center'],
                                       font=dict(color='white', size=12), height=25), columnwidth = [0.4, 0.4, 0.4, 0.4],
                           cells=dict(values=Temp, line_color='darkslategray', fill=dict(color=['WhiteSmoke', 'white']),
                                      align=['center', 'center'], font_size=12,height=20)), 1, 2)
    if Title != False:
        fig.update_layout(plot_bgcolor= 'white',
                      title={'text': Title, 'x':0.46, 'y':0.94, 'xanchor': 'center', 'yanchor': 'top'},
                          yaxis_title='Frequency')
    fig.show()
    
def Confusion_Matrix(Model, X, y, Labels, FG = (14, 5)):
    fig, ax = plt.subplots(1, 2, figsize=FG)
    y_pred = Model.predict(X)
    if y.shape[1] > 1:
        CM = confusion_matrix(y.argmax(axis = 1), y_pred.argmax(axis = 1))
    else:
        CM = confusion_matrix(y, np.round(y_pred))

    _ = sns.heatmap(CM.round(2), annot=True, annot_kws={"size": 14}, cmap="Blues", ax = ax[0])
    _ = ax[0].set_xlabel('Predicted labels')
    _ = ax[0].set_ylabel('True labels'); 
    _ = ax[0].set_title('Confusion Matrix');
    _ = ax[0].xaxis.set_ticklabels(Labels)
    _ = ax[0].yaxis.set_ticklabels(Labels)

    CM = CM.astype('float') / CM.sum(axis=1)[:, np.newaxis]
    _ = sns.heatmap(CM.round(2), annot=True, annot_kws={"size": 14}, cmap="Greens", ax = ax[1],
                   linewidths = 0.2, vmin=0, vmax=1, cbar_kws={"shrink": 1})
    _ = ax[1].set_xlabel('Predicted labels')
    _ = ax[1].set_ylabel('True labels'); 
    _ = ax[1].set_title('Normalized Confusion Matrix');
    _ = ax[1].xaxis.set_ticklabels(Labels)
    _ = ax[1].yaxis.set_ticklabels(Labels)
    return fig, ax

def Plot_Classification(Model, X, y, Labels, BP = .5, Alpha=0.6, ax = False, fs = 7, ColorMap =  'Spectral'):
    h=0.02
    pad=0.25
    # adding margins
    x_min, x_max = X[:, 0].min()-pad, X[:, 0].max()+pad
    y_min, y_max = X[:, 1].min()-pad, X[:, 1].max()+pad
    # Generating meshgrids
    xx, yy = np.meshgrid(np.arange(x_min, x_max, h), np.arange(y_min, y_max, h))
    # Predictions
    Pred = Model.predict(np.c_[xx.ravel(), yy.ravel()])
    if y.shape[1] > 1:
        Pred = Pred.argmax(axis = 1)
        
    Pred = Pred.reshape(xx.shape)
    # Figure
    if ax == False:
        fig, ax = plt.subplots(1, 1, figsize=(fs, fs))
    _ = ax.contourf(xx, yy, Pred, cmap = ColorMap, alpha=0.2)
    if y.shape[1] > 1:
        y = y.argmax(axis = 1)
    else:
        y = np.round(y).T[0]
    scatter = ax.scatter(X[:,0], X[:,1], s=70, c=y, edgecolor = 'Navy', alpha = Alpha, cmap = ColorMap)
    _ = ax.legend(handles=scatter.legend_elements()[0], labels= Labels,
                  fancybox=True, framealpha=1, shadow=True, borderpad=BP, loc='best', fontsize = 14)
    _ = ax.set_xlim(x_min, x_max)
    _ = ax.set_ylim(y_min, y_max)
    _ = ax.set_xlabel(r'$X_1$')
    _ = ax.set_ylabel(r'$X_2$')

Model Optimization Plot

Plot_history(Train_Table, Title = 'Train Set')
Plot_history(Validation_Table, Title = 'Validation Set')

Confusion Matrix

The confusion matrix allows for visualization of the performance of an algorithm.

fig, _ = Confusion_Matrix(model, X_train, y_train, Labels)
_ = fig.suptitle('Train Set', fontsize = 16)

fig, _ = Confusion_Matrix(model, X_test, y_test, Labels)
_ = fig.suptitle('Test Set', fontsize = 16)

Plot Classification

fig, ax = plt.subplots(1, 2, figsize=(16, 7))
# Train Set
Plot_Classification(model, X_train, y_train, Labels, BP = .2, ax = ax[0])
_ = ax[0].set_title('Train Set', fontsize = 16)
# Test Set
Plot_Classification(model, X_test, y_test, Labels, BP = .2, ax = ax[1])
_ = ax[1].set_title('Test Set', fontsize = 16)

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References

1. S. Jothilakshmi, V.N. Gudivada, in Handbook of Statistics, 2016
2. Keras developer guides
3. Multilayer perceptron wikipedia page
4. Confusion matrix wikipedia page

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